Optimisation of area

Hi guys, heres another great optimisation problem Just having a bit of trouble getting the right equations etc any help appreciated. Also as is stated in the brackets a net of the shape is required. As usual any help is appreciated. Thanx.

Question: Consider a rectangle of perimeter 60Cm. Form a cylinder by revolving this rectangle about one of its edges. What dimensions of the rectangle will result in a cylinder of maximum volume? (Include a net of the final shape)

To find: "What dimensions of the rectangle will result in a cylinder of maximum volume?"
So the dimensions of the rectangle when the first derivative of the volume of the cylinder is zero.

There are two possibilities: one is when the rectangle is revolved about one of its horizontal edges, and the other is when the rectangle is revolved about one of its vertical edges---if the 4 edges were either horizontal or vertical.

The net of the generated cylinder?
The surface area of the cylinder is a rectangle that is (10cm wide) by (2pi*20 cm long), or a rectangle 20cm by 40pi cm.

----If the net in question refers only to this suface area , then the net is a rectangle 10cm by 40pi cm.
----If the net in question includes also the 20cm by 10cm original rectangle,then the net is composed of two rectangles, side by side at their respective 10cm sides, a 10-by-20 and a 10-by-40pi. Or it is a longer rectangle that is 10cm by (20 +40pi)cm.
----If the net in question includes also the circular planes at each vertical side of the cylinder, then include two circles of radius 20cm each.

------------------------------------------------------------
1) When revolved about a vertical edge.

Let again vertical edges be x cm each, so the horizontal edges are (30-x) cm each.

Consider a rectangle of perimeter 60Cm.
Form a cylinder by revolving this rectangle about one of its edges.
What dimensions of the rectangle will result in a cylinder of maximum volume?
(Include a net of the final shape)

We have a rectangle with dimensions .

Code:

* - - - - - *
| |
W | |
| |
* - - - - - *
L

The perimeter is 60 cm: . .[1]

Revolve the rectangle about a vertical side.
The cylinder has radius and height .. . It volume is: .. . [2]